Here is the full list of all 51 X-Men Origins: Wolverine trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Raised one Mutagen to level 3
You found the cake, yummy!
Found 1/2 of all Dog Tags in the game
Defeated David Nord (Agent Zero)
Fought 4 W.E.N.D.I.G.0 prototypes at the same time and defeated them at Alkali lake.
Killed 200 enemies in Feral Sense
You feel a cold as you examine the sword and skeleton. A rustle of wind in the trees faintly echoes the name Arthas
Killed 25 Ghosts with their own weapon
Killed 30 enemies using objects in the environment
Lunged to 250 enemies
Killed 50 enemies while in Berserker mode
Dismembered 100 enemies
Killed 500 enemies
Performed a Wolverine to Wolverine Lunge
Killed 10 enemies using objects in the environment
Killed 10 enemies by throwing them off high areas
Escapes from Weapon X
Performed 10 Air Grabs
Killed 1 enemy with a reflected projectile
Lunged to 100 enemies
Lunged to a W.E.N.D.I.G.0 prototype's back
Defeated Victor Creed (Sabretooth)
Impaled Victor Creed outside the Bar
Killed 100 enemies
You found a mysterious hatch!
Lunged to 25 enemies
Performed 1 Counter move
Quick Killed 1 enemy
You collected all the trophies in Wolverine.
Defeated the Sentinel Mark I
Defeated Fred Dukes (The Blob)
Defeated Remy LeBeau (Gambit)
Defeated Weapon 11 (Deadpool)
Killed 2000 enemies
Quick Killed 20 enemies
Quick Killed 3 enemies in a row
Raised One Combat Reflex to Master Level
Raised All Combat Reflexes to Master Level
Found all Dog Tags in the game
Performed 25 Counter moves
Killed 25 enemies with a reflected projectile
Flew through the O ring in the Sentinel Boss Battle
Completed the Jungle Mission
Light 20 enemies on fire
Got 6 enemies airborne at once
Maxed out all upgrades
Killed 6 enemies with a single attack
Killed 200 enemies with Claw Spin
Beat the game on Hard Difficulty
Killed 150 enemies while in Berserker mode
Destroyed all objects in the grocery store fight with Fred Dukes (The Blob)